Multi-carrier modulation is an alternative to single-carrier broadband modulation for communications channels with frequency-dependent distortion. When used with rectangular pulse shaping, multi-carrier modulation and detection are efficiently implemented using the Fast Fourier Transform (FFT). An inverse FFT and FFT modulator/demodulator pair used in an OFDM technique enables channel equalization in the frequency domain, thus eliminating the need for potentially complex time-domain equalization of a single-carrier system. For this reason, OFDM is utilized in a number of systems, including wire-line digital subscriber loops (DSL), wireless digital audio and video broadcast (DAB, DVB) systems, and wireless local area networks (LANs) (e.g., IEEE 802.11 LANs). OFDM is also considered for fourth generation cellular systems and ultra-wideband (UWB) wireless communications in general.
While OFDM offers ease of channel equalization in the frequency domain, OFDM is sensitive to frequency offset. A frequency offset can result from a mismatch between the frequencies of the local oscillators, a Doppler distortion caused either by transmitter/receiver motion, or by a mismatch between transmitter and receiver sampling rates. An OFDM system can only tolerate a frequency offset that is significantly less than the carrier spacing, therefore frequency synchronization is used with OFDM systems. Any residual frequency offset causes loss of orthogonality between the carriers, and the resulting intercarrier interference (ICI) leads to performance degradation.
Algorithms have been proposed that are based on an assumption that the Doppler shift is equal for all subchannels. If the Doppler shift is caused by motion, the assumption is valid only for narrowband systems where the signal bandwidth B is substantially smaller than the center frequency fc. A Doppler distortion a which has a value normally much less than one causes the kth carrier frequency fk to be observed at the receiver as fk+afk. In a narrowband OFDM system with K carriers spaced at Δf such as represented by the example in FIG. 1A, fk is much greater than the signal bandwidth B which is KΔf, and the Doppler shift is approximately the same for all the carriers f1 to fk. In a wideband OFDM system such as represented by the example in FIG. 1B, the approximation is not valid, and the Doppler distortion causes different carriers f to experience substantially different frequency offsets.
Acoustic propagation occurs at low frequencies, therefore a high-rate underwater acoustic communications system is inherently wideband. In addition, the speed of sound in water is substantially lower than electromagnetic propagation through air or vacuum. Thus underwater acoustic communications are generally subject to severe motion-induced Doppler distortion. For a mobile underwater vehicle such as an autonomous underwater vehicle (AUV), the vehicle speed can be on the order of meters per second. Thus the Doppler rate for an AUV can be on the order of 0.001. Even in the absence of intentional motion, freely suspended transmitters and receivers are subject to drifting with waves and currents at a speed that can be less than a meter per second in calm conditions and at a speed of a few meters per second in rough seas. Consequently, Doppler shifting in a wideband acoustic system is not uniform across the signal bandwidth.
Underwater acoustic channels generally exhibit severe multipath propagation that produces a delay spread of a few milliseconds to more that 100 ms, depending on the communications system location and channel conditions. The channel is time varying with a Doppler spread that can be on the order of one Hz. High rate, bandwidth-efficient underwater acoustic communications traditionally use single-carrier modulation that relies on the use of adaptive multichannel processing based on joint phase synchronization and decision-feedback equalization; however, such communications require careful tuning of the receiver parameters. For example, the equalizer size and parameters of the digital phase-locked loop for each communications unit typically require tuning.
What is needed is a method for detection of wideband OFDM signals that addresses the above problems. The present invention satisfies this need and provides additional advantages.